Edited by: Carmen MolinaParis, University of Leeds, UK
Reviewed by: Tomasz Zal, University of Texas MD Anderson Cancer Center, USA; Joseph Reynolds, University of Leeds, UK
This article was submitted to T Cell Biology, a section of the journal Frontiers in Immunology.
This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Several reports in the literature have drawn a complex picture of the effect of treatments aiming to modulate IL2 activity
Several reports in the literature have drawn a complex picture of the effect of treatments aiming to modulate IL2 activity
Treatments that increase IL2 activity, simply by injecting it, have been shown to potentiate the immune response to vaccines (
Further complexity to the latter picture has been recently added with the preclinical assessment of treatments based on immunecomplexes formed by IL2 and monoclonal antibodies antiIL2. This treatment shows a much more potent
IL2 interacts with many different cells types, which express the three known chains of the IL2 receptor. Particularly relevant and complex is its relationship with the population dynamics of the CD4 T lymphocytes. IL2 was originally described as a potent CD4^{+} T cell growth factor (
To theoretically address the latter hypothesis, our group has developed mathematical models for Helper, Regulatory, and Memory T cells dynamics, which account for most wellknown facts relative to their relationship with IL2. We have simulated the effect of several types of therapies including the injection of: IL2; antibodies antiIL2; IL2/antiIL2 immunecomplexes, and mutants variants of IL2. We studied the qualitative and quantitative conditions of dose and timing for these treatments which allow them to potentiate either immunity or tolerance. Our results provide reasonable explanations for the existent preclinical and clinical data, predict some novel treatments, and further provide interesting practical guidelines to optimize the future application of these types of treatments.
The mathematical model used in this paper is based on the one developed in Ref. (
The concentration of soluble molecules in the blood compartment is assumed to decay with a constant characteristic rate, which represent renal elimination in the kidney. An external source term for these molecules is added in this compartment to simulate particular treatment applications. Interaction between free IL2 and antiIL2 antibodies are modeled in this and other compartments as a dynamic equilibrium characterized by a given biding affinity. Equations for the dynamics in this compartment are presented in “Dynamics in the Blood Compartment” in Appendix A.
The model includes, inside the lymph nodes, the dynamics of Helper (E), and Regulatory (R) T cells on three different functional states of their life cycle: resting, activated, and cycling cells. All the interactions involving these T cells occur in the presence of a constant amount of their cognate APCs and relevant homeostatic cytokines. The basic processes and interactions included in the model dynamics for these T cells are (see Figure
Resting E and R cells are produced at constant rate by the thymus; they die with a constant decay rate; they get activated (becoming an activated cell) following conjugation to their cognate APCs. The activation of E cells can be inhibited by the presence of colocalized R cells on the APCs.
The activated E and R cells could become cycling cells following a dosedependent response to cytokine derived signals. The activated R cells get this signal from the interaction with available IL2 while the E cells could additionally use other homeostatic cytokines
The cycling E and R cells are fully committed to divide, producing two new resting cells. Thus, they are presumed to do so with a constant rate.
The model includes also the dynamics of a generic population of nonCD4 T cells, which binds weakly to the existent APCs, but proliferates in response to IL2 signal, with similar sensitivity than the activated helper CD4^{+} T cells. This cells (referred as M cells) represent, the memory CD8^{+}CD44^{+} T cells, which can proliferate in response to IL2 without any requirements of activation by cognate APCs (see Figure
The dynamics of the number of T cells in the lymph node compartment, following the process described above, are modeled with the set of equations presented in “Dynamics of T Cells in the Lymph Node Compartment” in Appendix B.
The dynamics of IL2 molecules inside the lymph node takes into account the role of T cells in the production and degradation of this cytokine. The following processes are considered in the model [see Figure
IL2 is produced by E cells upon activation. It is produced as a burst whenever a resting E cell becomes an activated E cell. Such production of IL2 is inhibited, together with the E cell activation, by the presence of colocalized R cells on the APCs.
IL2 is degraded in the lymph nodes, after being internalized by the T cells in the form of complexes with the IL2 receptor at their cell surface.
Interactions of IL2 and T cells in the model are based on the expression by these cells, either in the resting, activated or cycling state, of different levels of the IL2 receptor. These receptors mediate the binding of IL2, which provide a stimulatory signal in a dosedependent fashion to the T cell. In this model the three known chains of the IL2 receptor, alpha, beta, and gamma (
IL2/IL2Receptor complexes formation is modeled as a multistep process: free, soluble, IL2 binds initially to the available free alpha or free beta chains of the receptor, and only then can form dimers or trimers with the remaining IL2 receptor chains at the cell membrane. The gamma chain is assumed to be always in excess compared with the amount of beta chain bound to IL2, either alone or together with alpha chain. Therefore gamma chain joins immediately to these membrane complexes, forming the well known intermediate (betagammaIL2) or high affinity (alphabetagammaIL2) IL2–IL2 receptor complexes.
IL2/IL2Receptor configurations, which include the beta and gamma chains (highaffinity alphabetagamma, and intermediate affinity betagamma receptor), trigger a signal into the T cells (
Beta and gamma chain of the IL2 receptor are similarly expressed by E and R cells in all functional states, but the expression of the alpha chain is modulated with T cell activation (
The M cells are assumed to express a negligible amount of the alpha chain of IL2 receptor, but have levels of the beta and gamma chain which are higher than those of helper and regulatory T cells (
Antibodies antiIL2 are modeled as molecules that can form complexes with the IL2, blocking or not its binding to the different chains of the IL2 receptor at the T cell surface. IL2 mutants are modeled as a molecule bearing similar properties than wildtype IL2, but differing in some specific parameter value on each case. In particular, we simulate the effects of IL2 mutants with an either reduced or increased Kon for the alpha or beta chains of the IL2R.
The equations in the model describing the dynamics of the number of molecules circulating in the Lymph Node (IL2, antiIL2 antibodies, and immunecomplexes) and the number of complexes IL2IL2R and IL2mAbIL2R formed in a single cell membrane are described in “Dynamics of Molecules in the Lymph Node” in Appendix C.
Four types of treatments are simulated in the model: injections of IL2; injections of antiIL2 monoclonal antibodies; injections of immune complex composed of a mixture of IL2 and antiIL2 antibodies with a specified constant proportion of them; and injection of mutant variants of IL2.
Treatments are simulated to represent a continuous infusion of the involved molecules for a defined period of time. This is implemented by setting on, transiently, the external source term of the molecules involved in a specific treatment (i.e., IL2; IL2m; and/or antiIL2 antibody). Two parameters always control treatment application: the “dose,” which set up the total amount per day of IL2, IL2m, and/or antiIL2 antibody infused; and the “treatment duration,” which set the time period for which continuous infusion is maintained. In all cases, we explore how the dose and treatment duration determine the outcome of the system simulation. We study whether or not different treatments can condition a significant preferential expansion (dominance) of helper T cells or regulatory T cells or M cells in the system.
Model parameters were previously calibrated in Ref. (
Variables  Definitions  

IL2_{S}  Total number of IL2 molecules in the blood  
IL2m_{S}  Total number of IL2m molecules in the blood  
Ab_{S}  Total number of antiIL2 mAb in the blood  
Total number of IL2mAb complexes in the blood  
IL2  Total number of free IL2 molecules (nonconjugated to IL2R at the cell membrane) in the lymph node  
IL2m  Total number of free IL2m molecules (nonconjugated to IL2R at the cell membrane) in the lymph node  
Ab  Total number of free antiIL2 mAb (nonconjugated to IL2IL2R complex at the cell membrane) in the lymph node  
IL2^{Ab}  Total number of free IL2mAb complexes (nonconjugated to IL2R at the cell membrane) in the lymph node  
Symbolic label that denotes the different IL2R chains: 

Symbolic label that denotes the possible functional states of the T cells: 

Γ 
External influx of IL2, typically used to simulate IL2 addition treatment  
Rate of IL2 production by helper CD4^{+} T cells upon activation  10^{3} M/h  
Elimination rate of IL2 in the blood  Ln(2)/10 min  
Total number of equivalent lymph nodes considered in the system  10  
Diffusion rate for the exchange of IL2 and mAbs, between the blood and peripheral lymph nodes  10^{−7} L ×Ln(2)/10 min  
Volume of the blood and lymph node compartments, respectively  2.5 × 10^{−3} L, 10^{−6} L  
fve  Fraction of the lymph node volume, in which molecules and mAbs can diffuse  0.1 
Association and dissociation constants of IL2mAb complexes  Face alpha mAb: 1.5 × 10^{5} M^{−1}s^{−1}, 1.4 × 10^{−4} s^{−1}; face beta mAb: 2.3 × 10^{4} M^{−1}s^{−1}, 6.6 × 10^{−5}s^{−1}  
Γ_{mi}  External influx of IL2m, typically used to simulate IL2 addition treatment  
Γ_{ab}  External influx of mAb, typically used to simulate antiIL2 mAbs addition treatment  
K_{da}  Elimination rate of mAbs and IL2mAbs complexes in the blood  Ln(2)/3 days 
Avogadro’s number  6,02 × 10^{23} mol^{−1} 
Variables  Definitions  

Total number (conjugated plus nonconjugated) of resting, activated, and cycling E cells  
Total number (conjugated plus nonconjugated) of resting, activated, and cycling R cells  
Total number (conjugated plus nonconjugated) of activated and cycling M cells  
Number of resting, activated, and cycling E cells conjugated to APCs  
Total number of conjugated E cells: 

Number of resting, activated, and cycling E cells nonconjugated to APCs: 

Number of resting, activated, and cycling R cells conjugated to APCs  
Total number of conjugated R cells: 

Number of resting, activated and cycling R cells nonconjugated to APCs: 

Number of activated and cycling M cells conjugated to APCs  
Total number of conjugated M cells: 

Number of activated and cycling M cells nonconjugated to APCs: 

Total number of APC conjugation sites that remain free in the system  
SigE, SigR, SigM  Number of bound cytokines signaling receptors at the surface of an activated 

Symbolic label that denotes the possible functional states of the T cells: 

Γ 
Input rate of new resting selfreactive E and R cells from the thymus  2.5 × 10^{4} cells/day 
Activation rate for resting E and R cells conjugated to APCs  Ln(2)/2 h, Ln(2)/6 h  
Division rate for cycling E, R, and M cells  Ln(2)/4 h  
IL2 signalingwaiting rate for activated E and R cells  Ln(2)/2 h  
IL2 signalingwaiting rate for activated M cells  Ln(2)/4 h  
Death rate for free resting E and R cells, and free activated M cells  Ln(2)/1 week  
Number of total APCs  2 × 10^{5}  
Total number of conjugations site per APC  5  
Equilibrium conjugation constants ( 

Equilibrium conjugation constants ( 

α_{E}, α_{R}  Fraction of activated E and R cells reverting to the resting state in the absence of cytokine related signal  0.95 
Hill coefficient at the sigmoid response curve  4  
Sensitivities thresholds for E, R, and M cells to cytokines signal  500 
Variables  Definitions  

Number of IL2 molecules bound to 

Number of IL2m molecules bound to 

Number of IL2/mAb complexes bound to the 

Number of IL2 molecules bound to high affinity IL2R (alpha + beta), at the surface of the indicated T cell type  
Number of IL2m molecules bound to high affinity IL2R (alpha + beta), at the surface of the indicated T cell type  
Number of IL2R of 

SigE, SigR, SigM  Number of cytokines signaling receptors at the surface of an activated 

Dissociation and association constant of IL2 to the 

Parameter that control the properties of different IL2m  10^{−3}, 10^{3}  
Switch parameter setting if the mAb blocks (=1) or not (=0) the interaction of IL2 with the 
0, 1  
Number of cytokine signaling receptors, at the surface of an activated 
10^{8}, 10^{7}  
Total number of alpha and beta chains of IL2R per E cells in the state 

Total number of alpha and beta chains of IL2R per R cells in the state 

Total number of alpha and beta chains of IL2R per M cells in the state 

Association and dissociation rates for the interaction of free beta chain to preformed IL2/alpha chain complexes, at the T cell membrane  
Association and dissociation rates for the interaction of free alpha chain to preformed IL2/beta chain complexes, at the T cell membrane  
Internalization (degradation) rate of signaling IL2/IL2R complex by T cells 
The simulations of the model dynamics was implemented using the program Mathematica v.4.0.
The model is setup to study the basic homeostasis of the immune system of a mouse (
Two main problems are then studied in the model simulations. (a) The basic dynamics states of the system in the absence of treatments; and (b) The effect of perturbations which represent specific IL2 modulation treatments on the stability of these dynamics states.
The model has two stable steady states which can be interpreted as natural tolerance and autoimmunity in the system. The steady state, which is interpreted as an autoimmune state (Figure
A key dynamical property of the model is the existence of a parameter regime where these steady states of tolerance and autoimmunity can coexist. This is a regime of bistable behavior (Figure
Moreover, it is important to note that the model reviewed here is an extension of the crossregulation model of immunity, which studies the interaction of helper and regulatory CD4^{+} T cells in the lymph node of the normal mice (
Regulatory T cells have to be more efficient using IL2 at low concentrations than helper and memory T cells.
The existence of a cytokine alternative to IL2 that promote helper T cell proliferation and survival.
The helper cells must become activated and proliferate more rapidly than Regulatory T cells in conditions of IL2 excess.
A detailed discussion of the validity of these constrains, from an experimental point of view, is provided in Ref. (
In following sections, the effects of different treatments, which aim to modulate IL2 activity, are studied. Treatments simulate a continuous infusion for a defined period of time of the involved molecules (IL2, IL2m, and/or antiIL2 antibody). Two parameters control their application: the “dose,” which set up the total amount per day of IL2, IL2m, and/or antiIL2 antibody infused; and the “treatment duration,” which set the time period of sustained infusion. Treatments are always applied in a system which is initially set to a dynamic equilibrium (i.e., either into the tolerant or the autoimmune steady state). We systematically study, whether a given treatment induces a significant change in the initial proportion of Regulatory (R) versus Helper (E + M) T cells, both transiently or permanently. We interpret that a treatment promotes immunity when it induces a transition from the tolerant steady state (dominated by R cells) to the autoimmune steady state (dominated by E cells). We interpret that a treatment promotes tolerance when it induces a transition from the autoimmune state to the tolerant steady state.
Simulations of IL2 injections show that, when this treatment is applied to a system initialized into the autoimmune steady state, it is unable to take the system into the tolerant steady state, irrespectively of the dose and treatment duration chosen. Moreover, it further promotes the expansion of the autoreactive E cells and the M cells (Figure
Thus overall in the model, IL2 injections appear to reinforce the preexistent steady state, this is expanding transiently either the R or the E cells respectively for a preexistent tolerant or autoimmune situation. A closer look to the model behavior qualitatively explains these results. Briefly: in a preexistent autoimmune steady state there is an excess of IL2 in the lymph node, thus is not lack of IL2 what limits regulatory T cell expansion, is their competition with autoreactive E cells for the cognate APCs. In consequence injecting IL2 would never reestablish tolerance. In a preexistent tolerant steady state, there is a small amount of IL2 in the lymph node, which is almost exclusively used by the regulatory T cells, limiting their expansion. The helper T cells do not expand as result of the direct suppression of their activation exerted by the R cells. In this situation the injection of IL2, naturally leads to the enhanced expansion of R cells reinforcing the suppression over the E cells. Only when the IL2 concentration is extremely high at the lymph nodes it triggers a significant expansion of the Memory T cells, signaling through the intermediate affinity IL2 receptor betagamma. The excessive expansion of the M cells in the system affects the suppressive interaction between E and R cells at the APCs, since these cells, although much weakly, also interact with and compete for the available APCs.
Interestingly the latter model predictions are indeed compatible with existent experimental observations and further provide a guideline for its future practical application. On the one hand, the reinforcement of ongoing immune reactions by IL2 injections, predicted by the model, explains classical observations on
On the other hand, the capacity of IL2 addition to reinforce natural tolerance mediated by regulatory T cells, predicted by the model, explains as well several experimental observations. Particularly, it explains clinical data stating that regulatory T cells populations are significantly expanded, both in cancer (
Furthermore, this second model prediction also explains many results in preclinical animal models. It explains, for instance, that IL2 injections can prevents allograft rejection (
AntiIL2 antibodies are molecules that form complexes with the IL2, blocking or not its binding to the different chains of the IL2 receptor at the T cell surface and therefore interfering with the associated signaling process. Three classes of antibodies are systematically explored in our simulations following its documented existence in the literature (
The injection of monoclonal antibodies antiIL2, in the model simulations, when applied to a previously tolerant system could induce a breakdown of tolerance (Figure
The effect of treatment with antiIL2 mAbs in a system with a preexistent autoimmune reaction is also quite significant. In this case, the treatment is capable of resetting the system into the tolerant steady state (i.e., inducing tolerance) (Figure
Overall the simulations of IL2 depletion treatments using antiIL2 antibodies predict that this type of therapy is able to break a preexistent tolerant state, inducing an autoimmune response, or to render tolerant a preexistent autoimmune system. A closer look to the model behavior qualitatively explains these results as follows. The injected mAbs appear to sequester the IL2, limiting its availability to provide signal to the T cells. When the treatment is applied into an initially tolerant steady state, the initial effective concentration of IL2 is low and it is further reduced to insignificant levels, where this cytokine is incapable to signal neither to E, R, or M cells. Therefore, if the treatment is sustained long enough, the number of R cells fall down to a minimum determined by the size of the thymic output, because the proliferation and survival of R cells is strictly dependent on IL2. But the number of E cells, on the other hand, set back to a value determined by the availability of the homeostatic cytokine of ILα, which they could use as alternative to IL2 signal. Therefore once the injected mAbs are cleared, the autoreactive E cells could have some initial advantage in respect to the R cells, leading the T cell expansion, which drive the system into the autoimmune steady state. However, when the treatment is applied to an initially autoimmune system, the effective concentration of IL2 is quite large and it is reduced by the presence of the antibody. The efficacy of the mAbs to affect IL2 signaling in the different T cell population is strongly dependent on its affinity for the IL2 and the side of the IL2 recognized. For a very high antibody dose, the effective IL2 concentration falls to negligible values, which as before are unable to signal neither to E, R, or M cells. Thus the size of the autoreactive E cell population is reduced to the value set by the availability of ILα and the number of R cell remains low in a value determined by the size of thymic output. When the injected antibody is cleared the system could return back to the autoimmune equilibrium. However, for some intermediate doses of the antibody, the effective IL2 concentration is reduced to values where it is unable to signal on the E and M cells, but it is still significant for the R cells, which are more sensitive due to their higher expression of the alpha chain of the IL2 receptor. Therefore, for these mAbs doses the E cell population is reduced to the minimal size, which can be sustained by the available ILα. But the R cells are stimulated to grow forcing the system to switch into the tolerant steady state.
The model prediction of a higher efficacy of treatments with face alpha mAbs, to break a preexistent tolerant steady state, relates to the impact of this type of mAbs on the dynamics of the M cells. Face alpha mAbs bind the available IL2 forming immunecomplexes that can still signal through the intermediate affinity IL2 receptor (beta + gamma chain). This form of the receptor is prevalent in the M cells, thus face alpha mAbs partially redirect IL2 signaling into the M cells expanding this population. The growth of the M cells interferes with the dynamics of CD4^{+} T cells, i.e., M cells consume the available IL2 and reduce the capacity of CD4^{+} T cells to interact with the APCs. The combination of the latter effects explains the advantage of the face alpha mAb to break a preexistent tolerant steady state. On the other hand, the differences observed between fully blocking and face beta mAbs in the model simulations (compare dose dependencies in Figure
Interestingly, the latter model predictions are indeed compatible with existent experimental observations. On the one hand, the predicted capacity of treatments blocking IL2 activity to promote autoimmunity/immunity, explains observations where monoclonal antibodies against IL2 have been shown to promote effective immune responses to tumors (
On the other hand, the model predicted capacity of IL2 blocking therapies to reestablish tolerance in the context of ongoing immune/autoimmune reactions, is not documented in the literature. This model prediction is very interesting from the practical perspectives for the treatment of autoimmune diseases. However, the fact that the predicted treatment effect just occurs for a particular intermediate range of antibody doses, applied during a relatively long period of time, makes difficult the practical implementation of the treatment. To overcome the latter problem we suggested, based on model simulations, an alternative/simpler strategy to capitalize this therapeutic effect. A large initial dose of the mAb could be used, reducing it periodically with a fixed rate. With this alternative strategy the model predict a much simpler dose dependency (see Figure
Immunecomplexes of IL2 plus antiIL2 mAbs (in a 1:2 mAb:IL2 molar proportion), has been recently highlighted as a novel therapeutic strategy (
In our simulations, immunecomplexes can either reinforce or weaken a preexistent tolerant steady state depending on the class of mAb used on its formulation. Figure
When applied to initially autoimmune steady states, all immunecomplexes fail to reestablish tolerance steady state. As the injection of IL2 the immunecomplexes further reinforce a preexistent autoimmune steady state, expanding the helper and memory T cells (Figure
Summarizing the results above shows that immune complex can sometimes synergistically potentiate the effects of IL2 and mAbs. Complexes based on face alpha mAbs do promote immunity primarily by expanding the M cells, and leading ultimately to a quite efficient breakdown of a preexistent tolerant steady state. Complexes based on face beta mAbs, can efficiently reinforce tolerance expanding significantly the R cells preexistent in the tolerant steady state. Face alpha mAbs for immunecomplexes are better with the highest possible affinity, but face beta mAbs could be better with some intermediate affinity values.
Qualitatively the effects of immunecomplexes can be explained based on two main dynamical properties in the model: (A) In the immune complex the IL2 is protected from degradation. While bind to the mAbs the IL2 has a life span of 3 days (like the mAbs), which is significantly larger than the life span of 10 min reported for free IL2. (B) Immunecomplexes block different sites in the surface of IL2 conditioning its preferential interaction with different cell populations, accordingly to their differential expression of the IL2 receptor chains. Face alpha mAbs, form immunecomplexes that bind and signal through the beta + gamma pair of IL2 receptors. Thus, since beta chain is overexpressed by the M cells, this complex preferentially redirect the IL2 signal to these cells. Following this analysis one could easily explain why this type of immune complex has a maximal efficiency when the affinity of the face alpha mAbs used is high. With high affinity mAbs, the IL2 is more protected from degradation, and the signaling is maximally redirected to the M cells. Face beta mAbs form immunecomplexes unable to signal in any class of IL2 receptor. Thus to mediate any biological activity this type of complex has to partially dissociate, working as a controlled source of free IL2. If the affinity of the face beta mAbs in the complex is too high then the IL2 is never released and the immunecomplexes have no effect at all. If the affinity of the face beta mAbs is too low, then injecting the complex is like injecting IL2 alone. However, if the affinity of the face beta mAbs in the complex is larger than the affinity of the dimeric IL2 receptor (beta + gamma chain), but lower than the affinity of the trimeric IL2 receptor (alpha + beta + gamma chain), the IL2 in the complex is easily release to provide signal through the high affinity trimeric IL2 receptor, but not through the intermediate affinity dimeric IL2 receptor. In this way the face beta based immunecomplexes provided a preferential signaling to the regulatory cells, which overexpress the alpha chain of the IL2 receptor.
Interestingly the model results explain available preclinical data on the use of immunecomplexes of IL2antiIL2 mAbs. Our observations that immunecomplexes formed with face alpha or face beta mAbs expand different cell populations when injected
The simulations, however, propose some interesting guidelines to improve the therapeutic effect of immunecomplexes. They predict that in the case of complexes using face alpha mAbs, the best strategy is to use mAbs with the higher affinity available. But in the case of immunecomplexes formed with face Beta or fully blocking mAbs, the use of intermediate affinity mAbs is recommended. Other important prediction of our model simulations is that treatment with immunecomplexes based on face beta or fully blocking mAbs are useful to reinforce a preexistent tolerant state preventing the induction of autoimmunity, but it would be quite inefficient to therapeutically treat an already established autoimmune disorder. For the later task, the best strategy would be to use the antiIL2 mAbs alone following the strategies described in Section “
Several mutant variants of IL2 have been designed aiming to improve the therapeutic efficacy of wildtype IL2 in cancer therapy. Most strategies, so far explored, involve the development of IL2 variants with an either reduced or increased binding affinity for the alpha or the beta chain of the IL2R. In this section three particular classes of mutants are simulated: (a) IL2 Mutant with a reduced conjugation affinity for the alpha chain of the IL2R as the one described in Ref. (
Figure
Figure
Overall the result in this section show that NoAlpha and BetaPlus IL2 mutants behave quite similarly, being significantly better than wildtype IL2 to promote immunity. While AlphaPlus mutants could be slightly better that wildtype IL2 to reinforce a preexistent tolerant state, expanding more the regulatory T cells. Qualitatively, the latter results could be easily understood in the model, by taking into account the differential expression of the high affinity/trimeric form (alpha + beta + gamma) and intermediate affinities/dimeric form (beta + gamma) of the IL2 receptors on the different T cell populations. Regulatory T cells, relay on the overexpression of the alpha chain of the IL2R, to have the highest expression of the high affinity form of the IL2R. Memory T cells relay in the overexpression of the beta chain of the IL2 R to have the higest expression level of the intermediate affinity form of the IL2R. The NoAlpha and BetaPlus mutants have a similar impact in the balance of use of IL2 related signal in the model. In both cases the resulting mutants lack the preferential capacity to signal over Regulatory T cells at low concentration, which is characteristic of the wildtype IL2. Furthermore they will preferentially redirect the signal toward the memory T cells, and strongly promote immunity. As the reverse case the AlphaPlus mutant, reinforce the capacity of the wildtype IL2 to signal preferentially over the Regulatory T cells, resulting on a better tool to reinforce a preexistent tolerance state.
The results obtained above are compatible with existent experimental data. Both Noalpha (
The predicted capacity of AlphaPlus mutants to reinforce preexistent tolerant steady state, expanding the regulatory T cells, has never been evaluated. A mutant variant of IL2 with 1000 times’ higher affinity for the IL2Ra was developed by Rao et al. (
Mathematical modeling of the IL2 and Tcell dynamics, considering the dual role of IL2 in its interaction with regulatory and helper CD4^{+} T cells, is able to explain the complexity observed in the effects of IL2 modulating treatments. In this sense, we show that the model explains a large amount of available clinical and preclinical data. Moreover, it predicts optimal strategies for the future application of these treatments:
Mutant variants of IL2, either with reduced affinity for CD25 (the alpha chain of IL2 receptor) or an increased affinity for CD122 (the beta chain of IL2 receptor), and with an increased life span in circulation (for instance fusing them to Fc portion of IgG), are the best strategy to potentiate immunity alone or in combination with vaccines.
Increasing IL2 life span in circulation, either by fusing it with larger proteins or forming complexes with mAbs that block the interaction of IL2 and CD122 (the beta chain of the IL2 receptor), significantly potentiate its capacity to reinforce a preexistent natural tolerance, further expanding the regulatory T cells. This effect might be useful to treat patients that would receive an organ transplant, reducing the risk of graft rejection.
AntiIL2 antibodies which block the interaction of IL2 with CD122, CD25, or both can be used to treat an ongoing autoimmune disorder, promoting the induction of tolerance. The best schedule for this therapy is to start treatment with a high dose of the mAb (one capable to induce some immune suppression) and then scale the dose down slowly the dose in subsequent applications.
Last, but not least, it is important to highlight that our model has focused on the control that IL2 exerts on T cell cycle progression, impacting both in T cell proliferation and survival. We have neglected some other reported roles of IL2 in T cell differentiation. For instance, IL2 has been reported to increase the suppressive capacity of the Regulatory T cells (
Moreover, severe toxicity, i.e., the appearance of the cytokine storm and the vascular leak syndrome, is perhaps the major limitation known today of the practical application of IL2 modulation treatments in clinics. Our model cannot be used to simulate directly the toxic effects of the different IL2 modulation treatments studied. It could only be used to predict strategies that optimize the expected therapeutic efficacy related to the balance between regulatory and effector CD4^{+} T cells. However, a recent report by the group of Boyman (
The authors dclare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Equations for the dynamics in the blood compartment are the following:
Equations
Equations
The dynamics of the number of T cells in the lymph node compartment, following the process described above, are modeled with the following set of equations:
The dynamics of the number of Helper and Regulatory CD4^{+} T cells, on their three different functional states of their life cycle [resting (
Equations
The Eqs
The equations in the model describing the dynamics of the number of molecules circulating in the Lymph Node (IL2, antiIL2 antibodies, and immunecomplexes) and the number of complexes IL2IL2R and IL2mAbIL2R formed in a single cell membrane are the following:
The dynamics of the number of IL2 (IL2), IL2 mutants (IL2m), mAbs (Ab), and immunecomplexes (IL2^{Ab}) in the lymph node is modeled using Eqs
In Eqs
The formation of high affinity IL2IL2R and IL2mIL2R complexes in a cell membrane is modeled as a twostep process, using equations (
The formation of IL2mAbIL2R complexes in the cell membrane is modeled in Eqs
^{1}Note that, although other cytokines are able to stimulate Tregs
^{2}Treatment using the face alpha mAbs is the best option (it work for lower MAb dose windows, example shown in Figure